View source for EvoLudoLab: Spatial Ecological PGG - Diffusion induced coexistence

{{EvoLudoLab:EcoPGG|
options="--module ePGG --model PDE --run --delay 100 --pdeN 101x --geometry nf --fitnessmap static 1,1 --colors red;green;black --timestep 1 --pdeD 100,1 --init circle 1,1,8 --groupsize 8 --cost 1.0 --interest 2.2 --deathrate 1.2 --dt 0.005 --pdeL 256"|
type=PDE|
title=Diffusion induced co-existence|
doc=The initial configuration is symmetric and gives rise to a symmetrical evolutionary end state. The competing forces of cooperators (activators) and defectors (inhibitors) gives rise to spatial pattern formation reminiscent of Turing patterns. However, in contrast to Turing's diffusion induced instability, diffusion induced co-existence develops in the vicinity of an unstable fixed point. Hence, in the absence of spatial extension, the population would disappear. Spatially heterogenous distributions enables cooperators and defectors to persist.

The parameters are <math>r=2.2</math>, <math>N=8</math>, <math>c=1</math>, <math>b=1</math>, <math>d=1.2</math> using numerical integration of the partial differential equation with the diffusion constants <math>D_C=1</math>, <math>D_D=100</math>. The initial configuration is a circular disk of equal densities of cooperators and defectors (<math>0.1</math>) in the center of a square lattice with fixed (reflecting) boundary conditions.

Note, in order to exactly reproduce the patterns emerging in the movie a finer mesh is required, i.e. smaller <math>dx</math>, and hence requires considerably more CPU time.}}

[[Category: Christoph Hauert]]